Does this program seem like one that'll have good employment prospects? How in-demand are "people with a strong real analysis background and a good knowledge of differential equations to work on financial derivatives" in the finance sector?

There is a real demand, but I couldn't really tell you how big it is. The Black-Scholes option pricing model is a PDE, and I understand that the name of the game is improving the basic model and then solving it numerically. I know they also hire people to work on asset allocation models.

My knowledge here is quite old, so if anybody else responds, listen to them instead